Deconvolution/1D: Difference between revisions
→{{header|jq}}
(19 intermediate revisions by 13 users not shown) | |||
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=={{header|11l}}==
{{trans|D}}
<
V result = [0]*(g.len - f.len + 1)
L(&e) result
Line 97:
V g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
print(deconv(g, f))
print(deconv(g, h))</
{{out}}
<pre>
[-8, -9, -3, -1, -6, 7]
[-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
</pre>
=={{header|Ada}}==
This is a translation of the '''D''' solution.
<syntaxhighlight lang="ada">with Ada.Text_IO; use Ada.Text_IO;
procedure Main is
package real_io is new Float_IO (Long_Float);
use real_io;
type Vector is array (Natural range <>) of Long_Float;
function deconv (g, f : Vector) return Vector is
len : Positive :=
Integer'Max ((g'Length - f'length), (f'length - g'length));
h : Vector (0 .. len);
Lower : Natural := 0;
begin
for n in h'range loop
h (n) := g (n);
if n >= f'length then
Lower := n - f'length + 1;
end if;
for i in Lower .. n - 1 loop
h (n) := h (n) - (h (i) * f (n - i));
end loop;
h (n) := h (n) / f (0);
end loop;
return h;
end deconv;
procedure print (v : Vector) is
begin
Put ("(");
for I in v'range loop
Put (Item => v (I), Fore => 1, Aft => 1, Exp => 0);
if I < v'Last then
Put (" ");
else
Put_Line (")");
end if;
end loop;
end print;
h : Vector := (-8.0, -9.0, -3.0, -1.0, -6.0, 7.0);
f : Vector :=
(-3.0, -6.0, -1.0, 8.0, -6.0, 3.0, -1.0, -9.0, -9.0, 3.0, -2.0, 5.0, 2.0,
-2.0, -7.0, -1.0);
g : Vector :=
(24.0, 75.0, 71.0, -34.0, 3.0, 22.0, -45.0, 23.0, 245.0, 25.0, 52.0, 25.0,
-67.0, -96.0, 96.0, 31.0, 55.0, 36.0, 29.0, -43.0, -7.0);
begin
print (h);
print (deconv (g, f));
print (f);
print (deconv (g, h));
end Main;
</syntaxhighlight>
{{output}}
<pre>
(-8.0 -9.0 -3.0 -1.0 -6.0 7.0)
(-8.0 -9.0 -3.0 -1.0 -6.0 7.0)
(-3.0 -6.0 -1.0 8.0 -6.0 3.0 -1.0 -9.0 -9.0 3.0 -2.0 5.0 2.0 -2.0 -7.0 -1.0)
(-3.0 -6.0 -1.0 8.0 -6.0 3.0 -1.0 -9.0 -9.0 3.0 -2.0 5.0 2.0 -2.0 -7.0 -1.0)
</pre>
Line 107 ⟶ 171:
{{works with|BBC BASIC for Windows}}
As several others, this is a translation of the '''D''' solution.
<
DIM h(5), f(15), g(20)
h() = -8,-9,-3,-1,-6,7
Line 144 ⟶ 208:
a$ += STR$(a(i%)) + ", "
NEXT
= LEFT$(LEFT$(a$))</
{{out}}
<pre>
Line 153 ⟶ 217:
=={{header|C}}==
Using [[FFT]]:
<
#include <stdlib.h>
#include <math.h>
Line 244 ⟶ 308:
for (int i = 0; i < lh; i++) printf(" %g", h2[i]);
printf("\n");
}</
{{out}}<pre>f[] data is : -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1
deconv(g, h): -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1
h[] data is : -8 -9 -3 -1 -6 7
deconv(g, f): -8 -9 -3 -1 -6 7</pre>
=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <algorithm>
#include <cstdint>
#include <iostream>
#include <vector>
void print_vector(const std::vector<int32_t>& list) {
std::cout << "[";
for ( uint64_t i = 0; i < list.size() - 1; ++i ) {
std::cout << list[i] << ", ";
}
std::cout << list.back() << "]" << std::endl;
}
std::vector<int32_t> deconvolution(const std::vector<int32_t>& a, const std::vector<int32_t>& b) {
std::vector<int32_t> result(a.size() - b.size() + 1, 0);
for ( uint64_t n = 0; n < result.size(); n++ ) {
result[n] = a[n];
uint64_t start = std::max((int) (n - b.size() + 1), 0);
for ( uint64_t i = start; i < n; i++ ) {
result[n] -= result[i] * b[n - i];
}
result[n] /= b[0];
}
return result;
}
int main() {
const std::vector<int32_t> h = { -8, -9, -3, -1, -6, 7 };
const std::vector<int32_t> f = { -3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1 };
const std::vector<int32_t> g = { 24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52,
25, -67, -96, 96, 31, 55, 36, 29, -43, -7 };
std::cout << "h = "; print_vector(h);
std::cout << "deconvolution(g, f) = "; print_vector(deconvolution(g, f));
std::cout << "f = "; print_vector(f);
std::cout << "deconvolution(g, h) = "; print_vector(deconvolution(g, h));
}
</syntaxhighlight>
{{ out }}
<pre>
h = [-8, -9, -3, -1, -6, 7]
deconvolution(g, f) = [-8, -9, -3, -1, -6, 7]
f = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
deconvolution(g, h) = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
</pre>
=={{header|Common Lisp}}==
Uses the routine (lsqr A b) from [[Multiple regression]] and (mtp A) from [[Matrix transposition]].
<
(defun make-conv-matrix (x m n)
(let ((lx (cadr (array-dimensions x)))
Line 274 ⟶ 387:
(A (make-conv-matrix f lg lh)))
(lsqr A (mtp g))))</
Example:
<
(setf h #2A((-8 -9 -3 -1 -6 7)))
(setf g #2A((24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7)))
Line 306 ⟶ 419:
(-2.0000000000000004)
(-7.000000000000001)
(-0.9999999999999994))</
=={{header|D}}==
<
int flen = f.length;
int glen = g.length;
Line 331 ⟶ 444:
writeln(deconv(g, f) == h, " ", deconv(g, f));
writeln(deconv(g, h) == f, " ", deconv(g, h));
}</
{{out}}
<pre>true [-8, -9, -3, -1, -6, 7]
Line 338 ⟶ 451:
=={{header|Fortran}}==
This solution uses the LAPACK95 library.
<
! Build
! Windows: ifort /I "%IFORT_COMPILER11%\mkl\include\ia32" deconv1d.f90 "%IFORT_COMPILER11%\mkl\ia32\lib\*.lib"
Line 412 ⟶ 525:
end program deconv
</syntaxhighlight>
Results:
<
deconv(f, g) = -8, -9, -3, -1, -6, 7
deconv(h, g) = -3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1
</syntaxhighlight>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="vbnet">Sub Deconv(g() As Double, f() As Double, h() As Double)
Dim As Integer n, i, lower
Dim As Integer hCount = Ubound(g) - Ubound(f) + 2
Redim h(hCount - 1)
For n = 0 To hCount - 1
h(n) = g(n)
lower = Iif(n >= Ubound(f) + 1, n - Ubound(f), 0)
i = lower
While i < n
h(n) -= h(i) * f(n - i)
i += 1
Wend
h(n) /= f(0)
Next n
End Sub
Dim As Integer i
Dim As Double h(5) = {-8, -9, -3, -1, -6, 7}
Dim As Double f(15) = {-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1}
Dim As Double g(20) = {24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7}
Dim As Double result()
Print !"h:\n[";
For i = Lbound(h) To Ubound(h)
Print h(i); ",";
Next i
Print Chr(8) & !"]\n";
Deconv(g(), f(), result())
Print !"\deconv(g, f):\n[";
For i = Lbound(result) To Ubound(result)-1
Print result(i); ",";
Next i
Print Chr(8) & !"]\n";
Print
Print !"f:\n[";
For i = Lbound(f) To Ubound(f)
Print f(i); ",";
Next i
Print Chr(8) & !"]\n";
Deconv(g(), h(), result())
Print !"\deconv(g, h):\n[";
For i = Lbound(result) To Ubound(result)-1
Print Using "##_,"; result(i);
Next i
Print Chr(8) & !"]\n";
Sleep</syntaxhighlight>
{{out}}
<pre>h:
[-8,-9,-3,-1,-6, 7]
deconv(g, f):
[-8,-9,-3,-1,-6, 7]
f:
[-3,-6,-1, 8,-6, 3,-1,-9,-9, 3,-2, 5, 2,-2,-7,-1]
deconv(g, h):
[-3,-6,-1, 8,-6, 3,-1,-9,-9, 3,-2, 5, 2,-2,-7,-1]</pre>
=={{header|Go}}==
{{trans|D}}
<
import "fmt"
Line 449 ⟶ 625:
}
return h
}</
{{out}}
<pre>
Line 459 ⟶ 635:
{{trans|C}}
<
import (
Line 523 ⟶ 699:
y[k], y[k+n/2] = y[k]+tf, y[k]-tf
}
}</
{{out}}
Some results have errors out in the last decimal place or so. Only one decimal place shown here to let results fit in 80 columns.
Line 533 ⟶ 709:
</pre>
'''Library gonum/mat:'''
<
import (
Line 568 ⟶ 744:
fmt.Printf("deconv(g, f) =\n%.1f\n\n", mat.Formatted(deconv(g, f)))
fmt.Printf("deconv(g, h) =\n%.1f\n", mat.Formatted(deconv(g, h)))
}</
{{out}}
<pre>
Line 599 ⟶ 775:
=={{header|Haskell}}==
<
deconv1d xs ys = takeWhile (/= 0) $ deconv xs ys
where
Line 641 ⟶ 817:
main :: IO ()
main = print $ (h == deconv1d g f) && (f == deconv1d g h)</
{{Out}}
<pre>True</pre>
Line 649 ⟶ 825:
This solution borrowed from [[Formal_power_series#J|Formal power series]]:
<
divide=: [ +/ .*~ [:%.&.x: ] +/ .* Ai</
Sample data:
<
f=: _3 _6 _1 8 _6 3 _1 _9 _9 3 _2 5 2 _2 _7 _1
g=: 24 75 71 _34 3 22 _45 23 245 25 52 25 _67 _96 96 31 55 36 29</
Example use:
<
_8 _9 _3 _1 _6 7
g divide h
_3 _6 _1 8 _6 3 _1 _9 _9 3 _2 5 2 _2 _7 _1</
That said, note that this particular implementation is slow since it uses extended precision intermediate results. It will run quite a bit faster for this example with no notable loss of precision if floating point is used. In other words:
<
=={{header|Java}}==
{{trans|Go}}
<
public class Deconvolution1D {
Line 698 ⟶ 874:
System.out.println(sb.toString());
}
}</
{{out}}
<pre>
Line 705 ⟶ 881:
f = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
deconv(g, h) = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
</pre>
=={{header|jq}}==
{{trans|Wren}}
'''Works with jq, the C implementation of jq'''
'''Works with gojq, the Go implementation of jq'''
'''Works with jaq, the Rust implementation of jq'''
<syntaxhighlight lang="jq">
def deconv($g; $f):
{ h: [range(0; ($g|length) - ($f|length) + 1) | 0] }
| reduce range ( 0;.h|length) as $n (.;
.h[$n] = $g[$n]
| (if $n >= ($f|length) then $n - ($f|length) + 1 else 0 end) as $lower
| .i = $lower
| until(.i >= $n;
.h[$n] -= .h[.i] * $f[$n - .i]
| .i += 1 )
| .h[$n] /= $f[0] )
| .h ;
### The tasks
def h: [-8, -9, -3, -1, -6, 7];
def f: [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1];
def g: [24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7];
h,
deconv(g; f),
f,
deconv(g; h)
</syntaxhighlight>
{{output}}
<pre>
[-8,-9,-3,-1,-6,7]
[-8,-9,-3,-1,-6,7]
[-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]
[-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1]
</pre>
Line 711 ⟶ 927:
Integer inputs may need to be converted and copied to floating point to use deconv().
<
g = [24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7]
f = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
Line 719 ⟶ 935:
fanswer = deconv(float.(g), float.(h))
println("The deconvolution deconv(g, h) is $fanswer, which is the same as f = $f\n")</
{{output}}
Line 730 ⟶ 946:
=={{header|Kotlin}}==
{{trans|Go}}
<
fun deconv(g: DoubleArray, f: DoubleArray): DoubleArray {
Line 756 ⟶ 972:
println("${f.map { it.toInt() }}")
println("${deconv(g, h).map { it.toInt() }}")
}</
{{out}}
Line 769 ⟶ 985:
=={{header|Lua}}==
Using metatables:
<
local h = setmetatable({}, {__index = function(self, n)
if n == 1 then self[1] = g[1] / f[1]
Line 783 ⟶ 999:
local _ = h[#g - #f + 1]
return setmetatable(h, nil)
end</
Tests:
<
local f = {-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1}
local g = {24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7}
local h = {-8,-9,-3,-1,-6,7}
print(unpack(deconvolve(f, g))) --> -8 -9 -3 -1 -6 7
print(unpack(deconvolve(h, g))) --> -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1</
=={{header|Mathematica}} / {{header|Wolfram Language}}==
This function creates a sparse array for the A matrix and then solves it with a built-in function. It may fail for overdetermined systems, though. Fast approximate methods for deconvolution are also built into Mathematica. See [[Deconvolution/2D%2B]]
<syntaxhighlight lang="mathematica">
deconv[f_List, g_List] :=
Module[{A =
Line 801 ⟶ 1,017:
Table[Band[{n, 1}] -> f[[n]], {n, 1, Length[f]}], {Length[g], Length[f] - 1}]},
Take[LinearSolve[A, g], Length[g] - Length[f] + 1]]
</syntaxhighlight>
Usage:
<pre>
Line 814 ⟶ 1,030:
The deconvolution function is built-in to MATLAB as the "deconv(a,b)" function, where "a" and "b" are vectors storing the convolved function values and the values of one of the deconvoluted vectors of "a".
To test that this operates according to the task spec we can test the criteria above:
<
>> g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7];
>> f = [-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1];
Line 827 ⟶ 1,043:
ans =
-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1</
Therefore, "deconv(a,b)" behaves as expected.
=={{header|Nim}}==
<
var h: seq[float] = newSeq[float](len(g) - len(f) + 1)
for n in 0..<len(h):
Line 848 ⟶ 1,064:
let g = [24'f64, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7]
echo
echo
echo
echo
{{out}}
<pre>
Line 862 ⟶ 1,078:
=={{header|Perl}}==
Using <code>rref</code> routine from [[Reduced row echelon form#Perl|Reduced row echelon form]] task.
{{trans|
<
use Math::Cartesian::Product;
sub deconvolve($g,$f) {
my(@m,@d);
Line 882 ⟶ 1,099:
}
sub convolve($f,$h) {
my @i;
for my $x (cartesian {@_} [0..$#f], [0..$#h]) {
Line 897 ⟶ 1,114:
}
sub rref($m) {
@m or return;
my ($lead, $rows, $cols) = (0, scalar(@m), scalar(@{$m[0]}));
$lead < $cols or return;
my $i = $r;
until ($m[$i][$lead]) {
$i = $r;
++$lead == $cols and return;
}
@m[$i, $r] = @m[$r, $i];
Line 916 ⟶ 1,134:
my @mr = @{ $m[$r] };
($lv, my $n) = ($m[$i][$lead], -1);
$_ -= $lv * $mr[++$n] foreach @{ $m[$i] };
}
++$lead;
}
}
Line 928 ⟶ 1,147:
print ' conv(f,h) = g = ' . join(' ', my @g = convolve(\@f, \@h)) . "\n";
print 'deconv(g,f) = h = ' . join(' ', deconvolve(\@g, \@f)) . "\n";
print 'deconv(g,h) = f = ' . join(' ', deconvolve(\@g, \@h)) . "\n";</
{{out}}
<pre> conv(f,h) = g = 24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7
Line 934 ⟶ 1,153:
deconv(g,h) = f = -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1</pre>
=={{header|
{{trans|D}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">deconv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lh</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lg</span><span style="color: #0000FF;">-</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lh</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lh</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">e</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">g</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">lf</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">e</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">/</span><span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">h</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">conv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">lf</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lh</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">lg</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lf</span><span style="color: #0000FF;">+</span><span style="color: #000000;">lh</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lg</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lh</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">lf</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span>
<span style="color: #000000;">g</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">h</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">g</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">h</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">f</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">24</span><span style="color: #0000FF;">,</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">71</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">34</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">22</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">45</span><span style="color: #0000FF;">,</span><span style="color: #000000;">23</span><span style="color: #0000FF;">,</span><span style="color: #000000;">245</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">52</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">67</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">96</span><span style="color: #0000FF;">,</span><span style="color: #000000;">96</span><span style="color: #0000FF;">,</span><span style="color: #000000;">31</span><span style="color: #0000FF;">,</span><span style="color: #000000;">55</span><span style="color: #0000FF;">,</span><span style="color: #000000;">36</span><span style="color: #0000FF;">,</span><span style="color: #000000;">29</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">43</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">7</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">desc</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">eq</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%s (%ssame as %s): %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">desc</span><span style="color: #0000FF;">,</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">==</span><span style="color: #000000;">e</span><span style="color: #0000FF;">?</span><span style="color: #008000;">""</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"**NOT** "</span><span style="color: #0000FF;">),</span><span style="color: #000000;">eq</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" conv(h,f)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"g"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">conv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">h</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span><span style="color: #000000;">g</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"deconv(g,f)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"h"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">deconv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g</span><span style="color: #0000FF;">,</span><span style="color: #000000;">f</span><span style="color: #0000FF;">),</span><span style="color: #000000;">h</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">test</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"deconv(g,h)"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"f"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">deconv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g</span><span style="color: #0000FF;">,</span><span style="color: #000000;">h</span><span style="color: #0000FF;">),</span><span style="color: #000000;">f</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
conv(h,f) (same as g): {24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7}
deconv(g,h) (same as f): {-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1}
</pre>
=={{header|PicoLisp}}==
<
(de deconv (G F)
Line 1,067 ⟶ 1,211:
(dec 'H
(*/ M (get F (- N I)) 1.0) ) )
(link (*/ H 1.0 A)) ) ) ) )</
Test:
<
F (-3. -6. -1. 8. -6. 3. -1. -9. -9. 3. -2. 5. 2. -2. -7. -1.)
G (24. 75. 71. -34. 3. 22. -45. 23. 245. 25. 52. 25. -67. -96. 96. 31. 55. 36. 29. -43. -7.)
Line 1,075 ⟶ 1,219:
(test H (deconv G F))
(test F (deconv G H))</
=={{header|Python}}==
Line 1,081 ⟶ 1,225:
Inspired by the TCL solution, and using the <code>ToReducedRowEchelonForm</code> function to reduce to row echelon form from [[Reduced row echelon form#Python|here]]
<
if not M: return
lead = 0
Line 1,134 ⟶ 1,278:
g = [24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7]
assert convolve(f,h) == g
assert deconvolve(g, f) == h</
Based on the R version.
<
import numpy
Line 1,179 ⟶ 1,323:
print(deconv(g,h))
</syntaxhighlight>
Output
Line 1,197 ⟶ 1,341:
* solution is ifft(fft(a)*fft(b)), truncated.
<
p <- length(a)
q <- length(b)
Line 1,214 ⟶ 1,358:
return(y[1:n])
}
</syntaxhighlight>
To check :
<syntaxhighlight lang="r">
h <- c(-8,-9,-3,-1,-6,7)
f <- c(-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1)
Line 1,226 ⟶ 1,370:
max(abs(deconv(g,f) - h))
max(abs(deconv(g,h) - f))
</syntaxhighlight>
This solution often introduces complex numbers, with null or tiny imaginary part. If it hurts in applications, type Re(conv(f,h)) and Re(deconv(g,h)) instead, to return only the real part. It's not hard-coded in the functions, since they may be used for complex arguments as well.
Line 1,232 ⟶ 1,376:
R has also a function convolve,
<syntaxhighlight lang="r">
conv(a, b) == convolve(a, rev(b), type="open")
</syntaxhighlight>
=={{header|Racket}}==
<
#lang racket
(require math/matrix)
Line 1,256 ⟶ 1,400:
(define lh (+ (- lg lf) 1))
(least-square (convolution-matrix f lg lh) g))
</syntaxhighlight>
Test:
<
(define f (col-matrix [-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1]))
(define h (col-matrix [-8 -9 -3 -1 -6 7]))
Line 1,265 ⟶ 1,409:
(deconvolve g f)
(deconvolve g h)
</syntaxhighlight>
{{out}}
<
#<array '#(6 1) #[-8 -9 -3 -1 -6 7]>
#<array '#(16 1) #[-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1]>
</syntaxhighlight>
=={{header|Raku}}==
(formerly Perl 6)
Translation of Python, using a modified version of the subroutine <code>rref</code> from [[Reduced row echelon form#Raku| Reduced row echelon form]] task.
<syntaxhighlight lang="raku" line>sub deconvolve (@g, @f) {
my \h = 1 + @g - @f;
my @m;
@m[^@g;^h] »+=» 0;
@m[^@g; h] »=« @g;
for ^h -> \j { for @f.kv -> \k, \v { @m[j+k;j] = v } }
(rref @m)[^h;h]
}
sub convolve (@f, @h) {
my @g = 0 xx + @f + @h - 1;
@g[^@f X+ ^@h] »+=« (@f X× @h);
@g
}
# Reduced Row Echelon Form simultaneous equation solver
# Can handle over-specified systems of equations (N unknowns in N + M equations)
sub rref (@m) {
@m = trim-system @m;
my ($lead, $rows, $cols) = 0, @m, @m[0];
for ^$rows -> $r {
return @m unless $lead < $cols;
my $i = $r;
until @m[$i;$lead] {
next unless ++$i == $rows;
$i = $r;
return @m if ++$lead == $cols;
}
@m[$i, $r] = @m[$r, $i] if $r != $i;
@m[$r] »/=» $ = @m[$r;$lead];
for ^$rows -> $n {
next if $n == $r;
@m[$n] »-=» @m[$r] »×» (@m[$n;$lead] // 0);
}
++$lead;
}
@m
}
# Reduce to N equations in N unknowns; a no-op unless rows > cols
sub trim-system (@m) {
return @m unless @m ≥ @m[0];
my (\vars, @t) = @m[0] - 1;
for ^vars -> \lead {
for ^@m -> \row {
@t.append: @m.splice(row, 1) and last if @m[row;lead];
}
}
while @t < vars and @m { @t.push: shift @m }
@t
}
my @h = (-8,-9,-3,-1,-6,7);
my @f = (-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1);
my @g = (24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7);
.say for ~@g, ~convolve(@f, @h),'';
.say for ~@h, ~deconvolve(@g, @f),'';
.say for ~@f, ~deconvolve(@g, @h),'';</syntaxhighlight>
{{out}}
<pre>24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7
24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7
-8 -9 -3 -1 -6 7
-8 -9 -3 -1 -6 7
-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1
-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1</pre>
=={{header|REXX}}==
<
call make
call make
call make
call show
call show
call show
call deco
call test
call deco
call test
exit
/*──────────────────────────────────────────────────────────────────────────────────────*/
deco
/*──────────────────────────────────────────────────────────────────────────────────────*/
make
/*──────────────────────────────────────────────────────────────────────────────────────*/
show
/*──────────────────────────────────────────────────────────────────────────────────────*/
test
{{out|output|text= when using the default internal inputs:}}
<pre>
array H: -8 -9 -3 -1 -6 7
array F: -3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1
array G: 24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7
</pre>
=={{header|RPL}}==
{{trans|D}}
When translating to RPL, it is mandatory to take into account that:
* array indexes start at 1
* For loop variables, j shall be preferred to i, which is the name of the internal constant that equals √-1
* FOR..NEXT loops are executed at least once
≪ → g f
≪ g SIZE f SIZE - 1 + 1 →LIST 0 CON
1 g 1 GET f 1 GET / PUT
2 OVER SIZE '''FOR''' n
g n GET
1 n f SIZE - 0 MAX +
n 1 - '''FOR''' j
OVER j GET
f n j - 1 + GET * -
'''NEXT'''
f 1 GET / n SWAP PUT
'''NEXT'''
≫ ≫ '<span style="color:blue">DECONV</span>' STO
≪ [-8 -9 -3 -1 -6 7]
[-3 -6 -1 8 -6 3 -1 -9 -9 3 -2 5 2 -2 -7 -1]
[24 75 71 -34 3 22 -45 23 245 25 52 25 -67 -96 96 31 55 36 29 -43 -7]
→ h f g
≪ g f <span style="color:blue">DECONV</span> h ==
g h <span style="color:blue">DECONV</span> f == AND
≫ ≫ ‘<span style="color:blue">TASK</span>’ STO
{{out}}
<pre>
1: 1
</pre>
=={{header|Scala}}==
{{Out}}Best seen running in your browser either by [https://scalafiddle.io/sf/ENWyl3Z/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/bFag8sS1Qr2Z062LN8dr6A Scastie (remote JVM)].
<
val (h, f) = (Array(-8, -9, -3, -1, -6, 7), Array(-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1))
val g = Array(24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7)
Line 1,341 ⟶ 1,592:
println(sb.result())
}</
=={{header|Swift}}==
{{trans|Kotlin}}
<syntaxhighlight lang="swift">func deconv(g: [Double], f: [Double]) -> [Double] {
let fs = f.count
var ret = [Double](repeating: 0, count: g.count - fs + 1)
for n in 0..<ret.count {
ret[n] = g[n]
let lower = n >= fs ? n - fs + 1 : 0
for i in lower..<n {
ret[n] -= ret[i] * f[n - i]
}
ret[n] /= f[0]
}
return ret
}
let h = [-8.0, -9.0, -3.0, -1.0, -6.0, 7.0]
let f = [-3.0, -6.0, -1.0, 8.0, -6.0, 3.0, -1.0, -9.0,
-9.0, 3.0, -2.0, 5.0, 2.0, -2.0, -7.0, -1.0]
let g = [24.0, 75.0, 71.0, -34.0, 3.0, 22.0, -45.0,
23.0, 245.0, 25.0, 52.0, 25.0, -67.0, -96.0,
96.0, 31.0, 55.0, 36.0, 29.0, -43.0, -7.0]
print("\(h.map({ Int($0) }))")
print("\(deconv(g: g, f: f).map({ Int($0) }))\n")
print("\(f.map({ Int($0) }))")
print("\(deconv(g: g, f: h).map({ Int($0) }))")</syntaxhighlight>
{{out}}
<pre>[-8, -9, -3, -1, -6, 7]
[-8, -9, -3, -1, -6, 7]
[-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
[-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]</pre>
=={{header|Tcl}}==
{{works with|Tcl|8.5}}
This builds the a command, <code>1D</code>, with two subcommands (<code>convolve</code> and <code>deconvolve</code>) for performing convolution and deconvolution of these kinds of arrays. The deconvolution code is based on a reduction to [[Reduced row echelon form#Tcl|reduced row echelon form]].
<
namespace eval 1D {
namespace ensemble create; # Will be same name as namespace
Line 1,444 ⟶ 1,740:
return $result
}
}</
To use the above code, a simple demonstration driver (which solves the specific task):
<
proc pp {name nlist} {
set sep ""
Line 1,463 ⟶ 1,759:
pp "deconv(g,f) = h" [1D deconvolve $g $f]
pp "deconv(g,h) = f" [1D deconvolve $g $h]
pp " conv(f,h) = g" [1D convolve $f $h]</
{{out}}
<pre>deconv(g,f) = h = [-8,-9,-3,-1,-6,7]
Line 1,477 ⟶ 1,773:
the same length by appending zeros to the short ones).
<
#import nat
Line 1,483 ⟶ 1,779:
deconv = lapack..dgelsd^\~&l ~&||0.!**+ band
</syntaxhighlight>
test program:
<
f = <-3.,-6.,-1.,8.,-6.,3.,-1.,-9.,-9.,3.,-2.,5.,2.,-2.,-7.,-1.>
g = <24.,75.,71.,-34.,3.,22.,-45.,23.,245.,25.,52.,25.,-67.,-96.,96.,31.,55.,36.,29.,-43.,-7.>
Line 1,496 ⟶ 1,792:
'h': deconv(g,f),
'f': deconv(g,h)>
</syntaxhighlight>
{{out}}
<pre>
Line 1,524 ⟶ 1,820:
-7.000000e+00,
-1.000000e+00>>
</pre>
=={{header|V (Vlang)}}==
{{trans|Go}}
<syntaxhighlight lang="v (vlang)">fn main() {
h := [f64(-8), -9, -3, -1, -6, 7]
f := [f64(-3), -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
g := [f64(24), 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96,
96, 31, 55, 36, 29, -43, -7]
println(h)
println(deconv(g, f))
println(f)
println(deconv(g, h))
}
fn deconv(g []f64, f []f64) []f64 {
mut h := []f64{len: g.len-f.len+1}
for n in 0..h.len {
h[n] = g[n]
mut lower := 0
if n >= f.len {
lower = n - f.len + 1
}
for i in lower..n {
h[n] -= h[i] * f[n-i]
}
h[n] /= f[0]
}
return h
}</syntaxhighlight>
{{out}}
<pre>
[-8, -9, -3, -1, -6, 7]
[-8, -9, -3, -1, -6, 7]
[-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
[-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
</pre>
=={{header|Wren}}==
{{trans|Go}}
<syntaxhighlight lang="wren">var deconv = Fn.new { |g, f|
var h = List.filled(g.count - f.count + 1, 0)
for (n in 0...h.count) {
h[n] = g[n]
var lower = (n >= f.count) ? n - f.count + 1 : 0
var i = lower
while (i < n) {
h[n] = h[n] - h[i]*f[n-i]
i = i + 1
}
h[n] = h[n] / f[0]
}
return h
}
var h = [-8, -9, -3, -1, -6, 7]
var f = [-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
var g = [24, 75, 71, -34, 3, 22, -45, 23, 245, 25, 52, 25, -67, -96, 96, 31, 55, 36, 29, -43, -7]
System.print(h)
System.print(deconv.call(g, f))
System.print(f)
System.print(deconv.call(g, h))</syntaxhighlight>
{{out}}
<pre>
[-8, -9, -3, -1, -6, 7]
[-8, -9, -3, -1, -6, 7]
[-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
[-3, -6, -1, 8, -6, 3, -1, -9, -9, 3, -2, 5, 2, -2, -7, -1]
</pre>
=={{header|zkl}}==
Using GNU Scientific Library:
<
fcn dconv1D(f,g){
fsz,hsz:=f.len(), g.len() - fsz +1;
Line 1,535 ⟶ 1,901:
h:=A.AxEQb(g);
h
}</
<
g:=GSL.VectorFromData(24,75,71,-34,3,22,-45,23,245,25,52,25,-67,-96,96,31,55,36,29,-43,-7);
h:=dconv1D(f,g);
Line 1,542 ⟶ 1,908:
f:=dconv1D(h,g);
f.format().println();</
{{out}}
<pre>
Line 1,550 ⟶ 1,916:
Or, using lists:
{{trans|D}}
<
flen, glen, delta:=f.len(), g.len(), glen - flen + 1;
result:=List.createLong(delta); // allocate list with space for items
Line 1,560 ⟶ 1,926:
}
result;
}</
<
f:=T(-3,-6,-1,8,-6,3,-1,-9,-9,3,-2,5,2,-2,-7,-1);
g:=T(24,75,71,-34,3,22,-45,23,245,25,52,25,-67,
-96,96,31,55,36,29,-43,-7);
println(deconv(g, f) == h, " ", deconv(g, f));
println(deconv(g, h) == f, " ", deconv(g, h));</
{{out}}
<pre>
|